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Imagine a 3x3x3 wooden cube. How many cuts do we need to break it into twenty-seven 1x1x1 cubes? A cut may go through multiple wooden pieces.
Explanation :
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X axis - 2 cuts, 3 pieces
then Y axis - 2 cuts, 3*3 = 9 pieces
now, Z axis - 2 cuts, 3*3*3 = 27 pieces.
The central 1×1×1 cube has six faces. No cut can reveal two or more of these faces! So six cuts are necessary and sufficient.
